We determine the critical strength of the effective electric coupling for the onset of Bose condensation of stable magnetic monopoles and antimonopoles in SU(2) Yang-Mills thermodynamics. Two scenarios are considered: infinitely fast and infinitely slow downward approach of the critical temperature. Our results support the claim that the first lepton family and the weak interactions emerge from pure SU(2) gauge dynamics of scale $\sim 0.5 $MeV.
The interaction of a magnetic monopole-antimonopole pair depends on their separation as well as on a second "twist" degree of freedom. This novel interaction leads to a non-trivial bound state solution known as a sphaleron and to scattering in which the monopole-antimonopole bounce off each other and do not annihilate. The twist degree of freedom also plays a role in numerical experiments in which gauge waves collide and create monopole-antimonopole pairs. Similar gauge wavepacket scatterings in the Abelian-Higgs model lead to the production of string loops that may be relevant to superconduct…
We investigate the monopole-antimonopole pair solution in the SU(2) x U(1) Weinberg-Salam theory with $ϕ$-winding number, $n=3$ for bifurcation phenomena. The magnetic monopole merges with antimonopole to form a vortex ring with finite diameter at $n=3$. Other than the fundamental solution, two new bifurcating solution branches were found when Higgs coupling constant $λ$, reaches a critical value $λ_c$. The two new branches possess higher energies than the fundamental solutions. These bifurcating solutions behave differently from the vortex ring configuration in SU(2) Yang-Mills-Higgs theory s…
We investigate further the properties of axially symmetrical monopole-antimonopole pair in the standard Weinberg-Salam theory. These numerical solutions behave quite differently from their counterparts in the SU(2) Yang-Mills-Higgs theory as the poles are now bounded by a flux string. Our results confirm that the energy of these solutions resides in a range of 13.17 - 21.02 TeV. In addition, we found strong evidence suggesting this configuration is time-dependent and discovered an energy oscillation phenomenon between the monopole and anti-monopole, which is associated with the symmetry of the…
We numerically study the interactions of twisted monopole-antimonopole pairs in the 't Hooft-Polyakov model for a range of values of the scalar to vector mass ratio. We also recover the sphaleron solution at maximum twist discovered by Taubes, and map out its energy and size as functions of parameters.
We show that monopoles can be pair produced by cosmological magnetic fields in the early universe. The pair production gives rise to relic monopoles, and at the same time induces a self-screening of the magnetic fields. By studying these effects we derive limits on the monopole mass, and also on the initial amplitude of primordial magnetic fields. Monopoles of GUT scale mass can even be produced if primordial magnetic fields exist at sufficiently high redshifts.
The dynamics of an electric charge $e$ in presence of a fixed monopole pair $\pm g$ is considered. Depending on the ratio of the angular momentum to $e\,g/c$, the effective potential may consist a minimum valley between the poles or a finite depth well. In the classical limit the charge may be bound to the poles inside the minimum valley or well. In the quantum theory, due to the finite barrier between the minimum and the potential at infinity, only approximate or quasi bound-states are possible. Based on the Rayleigh-Ritz variational method the energy and eigen-functions are obtained. The imp…
We propose a new class of regular stationary axially symmetric solutions in a pure QCD which correspond to monopole-antimonopole pairs at macroscopic scale. The solutions represent vacuum field configurations which are locally stable against quantum gluon fluctuations in any small space-time vicinity. This implies that the monopole-antimonopole pair can serve as a structural element in microscopic description of QCD vacuum formation through the monopole pair condensation.
Topological Stabilization via Higgs and $Z$-Boson Mediated Repulsions in Electroweak Monopole-Antimonopole Pairs
Southern Center for Nuclear Science Theory, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；School of Physics, Universiti Sains Malaysia（马来西亚理科大学物理学院）
Gauge field configuration for a magnetic monopole and its dual configuration are studied in SU(2) gauge theory. We present a relation between the monopole field and its dual field. Since these fields can become massive, their massive Lagrangians are derived. In the dual case, an additional term appears. We show this term is necessary to produce a linear potential between a monopole charge and an antimonopole charge.
We use the $SU(5)$ model to show the presence in grand unified theories of an electroweak monopole and a magnetic dumbbell ("meson") made up of a monopole-antimonopole pair connected by a $Z$-magnetic flux tube. The monopole is associated with the spontaneous breaking of the weak $SU(2)_L$ gauge symmetry by the induced vacuum expectation value of a heavy scalar $SU(2)_L$ triplet with zero weak hypercharge contained in the adjoint Higgs 24-plet. This monopole carries a Coulomb magnetic charge of $(3/4) (2π/e)$ as well as $Z$-magnetic charge, where $2π/e$ denotes the unit Dirac magnetic charge. …
We present a direct Monte-Carlo determination of the scaling dimension of a topological defect operator in the infrared fixed point of a three-dimensional interacting quantum field theory. For this, we compute the free energy to introduce the background gauge field of the $Q=1$ monopole-antimonopole pair in three-dimensional non-compact QED with $N=2,4$ and $12$ flavors of massless two-component fermions, and study its asymptotic logarithmic dependence on the monopole-antimonopole separation. We estimate the scaling dimension in the $N=12$ case to be consistent with the large-$N$ (free fermion…
